Next-to-Leading Order Unitarity Fits in the Extended Georgi-Machacek Model

TL;DR

This paper performs a detailed theoretical and phenomenological analysis of the extended Georgi-Machacek model, including one-loop unitarity bounds, stability conditions, and fits to LHC Higgs data, to constrain its parameter space.

Contribution

It introduces NLO unitarity bounds and efficient BFB conditions for the extended GM model, and performs a global fit to Higgs data to constrain model parameters.

Findings

NLO unitarity bounds significantly constrain quartic couplings.

Bounded-from-below conditions are efficiently approximated by 3-field analysis.

Mass differences among heavy Higgs bosons are constrained to be less than 410 GeV.

Abstract

The Georgi-Machacek (GM) model is a triplet scalar extension of the Standard Model (SM) that preserves custodial symmetry (CS) due to an explicit global $SU(2)_L\otimes SU(2)_R$ symmetry in the scalar potential at tree-level. However, it is also possible to construct a triplet extended scalar sector of the SM without imposing this global symmetry in the potential while still maintaining CS at tree-level. This is referred to as the extended GM (eGM) model. We compute one-loop corrections to all $2\to2$ bosonic scattering amplitudes in both models and place next-to-leading order (NLO) unitarity bounds on the quartic couplings. Further, we derive the bounded-from-below (BFB) conditions on the quartic couplings demanding the stability of the scalar potential in the field subspaces. We show that the 3-field BFB conditions provide a very good approximation of the 13-field BFB conditions for both models and are computationally more efficient. With these theoretical constraints, we perform a global fit of both models to the latest Higgs signal strength results from the $13$ TeV Large Hadron Collider. We observe that the global fit disfavors the regions where $\kappa_V > 1.05$, $\kappa_V < 0.95$, and $\kappa_f > 1.05$, $\kappa_f< 0.92$ at a $95.4\%$ CL for both models. The global fit results demonstrate that NLO unitarity and stability bounds play a significant role in constraining the allowed parameter space of both models. We obtain an upper limit on the absolute values of the scalar quartic couplings to be $1.91\:(2.51)$ in the GM (eGM) model. We find that in both models, the absolute mass differences between the heavy Higgs bosons are less than $410$ GeV if their masses are below $1.1$ TeV. The maximal mass difference among the members of each CS multiplet is less than $210$ GeV in the eGM model.